36
12. Simplify
V ?
(1) 49
LINV 10
(4) 121
(2) 64
(3) 81
Answers
Step-by-step explanation:
We know that 69 and 96 are having ten’s and unit’s place interchanged, i.e., they are having reverse digits.
So, sum of digits is 15.
We know that when ab + ba is divided by 11 then quotient is (a + b).
∴ The sum of 69 and 96 is divided by 11 then we get 15 (sum of digits) as our quotient.
(ii) 15
We know that 69 and 96 are having ten’s and unit’s place interchanged, i.e., they are having reverse digits.
So, sum of digits is 15.
We know that when ab + ba is divided by (a + b) then quotient is 11.
∴ The sum of 69 and 96 is divided by 15 (sum of digits) then we get 11 as our quotient.
Answer:
Think of the numbers before the equal signs as the numbers associated with terms in a series. Thus, term 2 1s 6, term 3 is 12, term 4 is 20, term 5 is 30, and term 6 is 42. Notice that the differences between successive terms is a sequence of steadily increasing even numbers, i.e. term 3 = term 2 + 6, term 4 = term 3 + 8, term 5 = term 4 + 10, term 6 = term 5 +12. If this is really the pattern producing these numbers, we can proceed as follows:
term 7 = term 6 + 14 = 42 + 14 = 56; term 8 = term 7 + 16 = 56 + 16 = 72, and to answer your question
term 9 + term 8 + 18 = 72 + 18 = 90, and you are correct.
Notice that we could also work backwards to find term 1 = 2, and term 0 = 0, and these terms fit the same pattern. Finally, notice that there are several other ways to represent the terms in this pattern, including the following:
term n = n(n + 1); term n = n + n^2; term n = 2 (0 + 1 + 2 + 3 + … + n), etc.
Step-by-step explanation: